Brilliant Series!

Algebra Level 3

\[ 3 \dbinom{n}{0} - 8\dbinom{n}{1}+13 \dbinom{n}{2} - 18 \dbinom{n}{3} + \ldots \pm (3+5n) \dbinom {n}{n} \]

What is the value of the summation above for positive integer \(n \geq 2 \)?

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